Question

problem 5: select expressions that could represent the slope of this line. (0,5) (4,6) (8,7) (16,9)

Explanation:

Step1: Recall Slope Formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Use Points (0, 5) and (4, 6)

Calculate slope: \( \frac{6 - 5}{4 - 0} = \frac{1}{4} \).

Step3: Use Points (4, 6) and (8, 7)

Calculate slope: \( \frac{7 - 6}{8 - 4} = \frac{1}{4} \).

Step4: Use Points (8, 7) and (16, 9)

Calculate slope: \( \frac{9 - 7}{16 - 8} = \frac{2}{8} = \frac{1}{4} \) (simplify \( \frac{2}{8} \) to \( \frac{1}{4} \)). Also, \( \frac{4}{16} \) (if we take larger differences, e.g., from (0,5) to (16,9): \( \frac{9 - 5}{16 - 0} = \frac{4}{16} = \frac{1}{4} \)).

Check each option:

• \( \frac{1}{4} \): Matches (from Step2,3,4).
• \( \frac{4}{16} \): Simplifies to \( \frac{1}{4} \), matches.
• \( \frac{2}{8} \): Simplifies to \( \frac{1}{4} \), matches.

Answer:

The expressions that represent the slope are \( \boldsymbol{\frac{1}{4}} \), \( \boldsymbol{\frac{4}{16}} \), and \( \boldsymbol{\frac{2}{8}} \) (assuming the checkboxes correspond to these; based on calculation, these equal \( \frac{1}{4} \), the slope of the line).